Question

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Answer 1

`h\:=\:\:(-\pi \:kr\:+\:S)/(\pi \:r)`

Explanation:

Given the expression

`S=\pi \:r\left(h+k\right)\:`

• Let us solve for h

`S=\pi \:r\left(h+k\right)\:`

Flip the equation

`\pi r\left(h+k\right)\:=\:S`

Apply distributive law:
`a\left(b+c\right)=ab+ac`

`\pi hr+\pi kr=S`

Add -πkr to both sides

`\pi hr+\pi kr+\left(-\pi kr\right)=S+\left(-\pi kr\right)`

`\pi hr\:=\:-\pi kr\:+\:S`

Divide both sides by πr

`\pi hr\:/\:\pi r\:=\:\:(-\pi \:kr\:+\:S)/(\pi \:r)`

`h\:=\:\:(-\pi \:kr\:+\:S)/(\pi \:r)`

Therefore, we conclude that:

`h\:=\:\:(-\pi \:kr\:+\:S)/(\pi \:r)`